🧮 algebra

1. **State the problem:** Solve the equation $$x^2 + \frac{2^{x-5}}{3} - \frac{1}{3}x - \frac{2(x-25)}{15} = 2x + \frac{3}{5} + 2x + (x-1)^2$$. 2. **Rewrite and simplify the equati

1. Solve each equation and classify it. (a) Solve $$\frac{1}{2}x + 6 = \frac{3}{4}x - 2 - \frac{1}{4}x + 8$$

1. The problem is to simplify the expression $23\sqrt{94}$. 2. The expression consists of a coefficient 23 multiplied by the square root of 94.

1. The problem is to express a given number or expression as a fraction. 2. To convert a decimal or mixed number to a fraction, identify the place value of the last digit.

1. **State the problem:** We have a total investment of 20000 split into two parts: one part invested at 11% simple interest for 2 years, and the other part invested at 8% simple i

1. **State the problem:** Solve the equation $8x - 40 = 20x - 4$ for $x$. 2. **Write the formula and rules:** To solve linear equations, we isolate the variable $x$ by performing t

1. **State the problem:** Solve the inequality $$\frac{x^2+5x+6}{x+3} > 0$$. 2. **Factor the numerator:** The quadratic $x^2+5x+6$ factors as $$(x+2)(x+3)$$.

1. **State the problem:** We have a rectangle with sides $2x$ and $4x$, and the area $A$ satisfies the inequality $32 < A < 392$. 2. **Formula for area of a rectangle:**

1. **State the problem:** Solve the equation $6(x-4)=2x+4$ for $x$. 2. **Write down the formula and rules:** Use the distributive property to expand and then isolate $x$ by combini

1. **Nyatakan masalah:** Diberi fungsi kuadratik $$f(x) = 2(x^2 - x - 2)$$.

1. El problema trata sobre la agrupación y factorización de expresiones algebraicas. 2. La agrupación consiste en agrupar términos que tienen factores comunes para luego factorizar

1. **State the problem:** Simplify the expression $6px + 10py + 18qx + 30qy$ by factoring common terms. 2. **Identify common factors:** Group terms with common variables:

1. Probleem: Vul de ontbrekende gegevens in de tabel aan met behulp van verhoudingstabellen. 2. Formule: Snelheid = Afstand / Tijd

1. ปัญหาคือการแก้อสมการเชิงเส้นสองตัวแปร เช่น $ax + by \leq c$ หรือ $ax + by > d$ ซึ่งเป็นอสมการที่มีตัวแปร $x$ และ $y$ อยู่ด้วยกัน 2. สูตรทั่วไปของอสมการเชิงเส้นสองตัวแปรคือ $$ax

1. **ปัญหา:** ฝ้ายซื้อแก้วน้ำใบเล็กและใบใหญ่รวมกัน 50 ใบ รวมเป็นเงิน 3450 บาท 2. **กำหนด:**

1. **Solve the system of equations using the graphical method:** Given:

1. Planteamos el problema: Una cantidad $N$ se reparte en forma directamente proporcional a los números 5, 9 y 7. 2. Esto significa que las partes son $5x$, $9x$ y $7x$ para algún

1. **Problem:** Simplify the ratio 36:90 to its lowest terms. **Formula:** To simplify a ratio, divide both terms by their greatest common divisor (GCD).

1. **Problem:** Simplify the ratio 36:90 to its lowest terms. 2. **Formula:** To simplify a ratio, divide both terms by their greatest common divisor (GCD).

1. The problem is to find the value of $x$ in the equation $2x + 3 = 11$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. Planteamos el problema: Dada la función $A(x) = x^2 - 5x + 6$, debemos encontrar los valores de $x$ para los cuales el número de asistentes está entre 0 y 10 unidades, es decir,